The disease triangle (Figure 1) is one of the first concepts encountered by college students in an introductory plant pathology course (1) and often may be re-encountered in higher level classes as a fundamental principle of the factors involved in disease causation. Thus, the figure illustrates one of the paradigms in plant pathology; that is, the existence of a disease caused by a biotic agent absolutely requires the interaction of a susceptible host, a virulent pathogen, and an environment favorable for disease development (1,6). Conversely, plant disease is prevented upon elimination of any one of these three causal components.

Figure 1. The equilateral plant disease triangle after Stevens (6). The three necessary causal factors of disease are positioned at the vertices.

This triangular relationship is unique to phytopathology in comparison to veterinary and medical sciences because terrestrial plants possess little thermal storage capacity and their immobility precludes escape from an inhospitable environment. The sophisticated immune system found in mammals is absent in plants, and this places an emphasis on the host's genetic constitution. Finally, the predominance in phytopathology of fungi, which are also highly dependent on environment, may have contributed to the development of this paradigm.

The disease triangle drawing most likely was first published by Stevens in 1960 (6), although earlier plant pathologists certainly recognized the interaction among plant, pathogen, and environment. For example, Duggar (4) wrote in 1909: ". . . the abundance of a very large number of fungous [sic] diseases is directly connected with or conditioned by climatologicalfactors . . . factors may affect independently host and parasite, and they may affect the interrelations of these organisms." However, perhaps none of these pioneering plant pathologists prior to Stevens was so explicit in their treatment of this three-way interaction as Gäumann (5), who analyzed examples of crucial environmental, host, and pathogen determinants and their effects on disease development.

In a qualitative sense, the disease triangle concisely illustrates the phenomenon of plant disease as occupying the interior space of a triangle with the three essential factors at the vertices (Figure 1). Alternatively, the three factors may be associated with the line segments (i.e., triangle sides); then, line length and interior volume can show variation in the strength of the relationship in a quantitative sense (Figure 2). For example, a host with some degree of resistance, but not immune, will result in an overall lower level of disease. Used in this sense, the disease triangle illustrates the continuum of host reaction from complete susceptibility to immunity. So too, the degree of pathogen virulence and environmental conduciveness may be conveyed equally well. If any one element is reduced to a null variable, the geometric figure transforms into a line and the area occupied by disease collapses to zero. Aside from this null case, the alternative quantitative representation (Figure 2) treats disease as a degree of intensity (i.e., incidence or severity) rather than as a phenomenon.

Figure 2. A variant representation of the plant disease triangle showing an unequal relationship among the environment, pathogen and host determinants, which are associated with line segments.

Some plant pathologists have elaborated on the disease triangle by adding one or more parameters (1). Suggested additional parameters have included humans, vectors, and time. Of these, only time is absolutely required so other elements represent special case applications. A three-dimensional disease pyramid or tetrahedron (Figure 3) has been the most common figure drawn after addition of a single parameter. Adding more than one parameter while retaining the pyramidal shape is possible by drawing a base with four line segments. The disadvantage for such a figure lies in that the two opposing vertices (or parallel lines) of the four basal factors are shown to interact indirectly. Interaction among five factors was conveyed by Agrios (1) as a tetrahedron with a vertical line extending from the base to the upper vertex.

Figure 3. A disease pyramid or tetrahedron, which allows for the addition of a fourth causal factor of disease.

Humans factor into the disease triangle because the influence of human activity on disease is pervasive in agriculture and, perhaps to a lesser degree, in lower input systems such as forestry and range management. Indeed, it is difficult to ignore such elements as cultivation practices that affect a pathogen's life cycle, genetic manipulation of plant hosts through breeding and genetic engineering, planting large expanses of genetically similar plant populations, and various environmental manipulations such as irrigation, greenhouses, and hydroponics. These factors can profoundly affect the occurrence and severity of a particular disease.

The argument against including humans as a disease triangle factor views domesticated plants as already having their identity intimately intertwined with husbandry and so humans already are represented implicitly in the triangle configuration. Certainly, many crops such as corn (maize) no longer exist in the wild or scarcely resemble wild relatives. Secondly, humans constitute a part of the pathosystem environment in the sense that we are external to the host-parasite interaction. Thus, regardless of our dominant influence, a view devoting a dimension to ourselves may be considered anthropocentric.

Animal and other vectors may not be essential for all diseases but certainly play a critical role in many. Thus, vectors represent a special case for modification of the triangular relationship. In some cases, the pathogen actually multiplies within the cells of a vector and so disease transmission would be severely inhibited without this stage in its life cycle. However, if the pathogen is incapable of infecting its host without a vector, the pyramid fails to show adequately the intermediary nature of the vector in the pathogen-plant relationship by drawing a direct connection and circumventing the vector. Perhaps an illuminating alternative diagram would have the vector occupying the disease triangle side that connects the host and pathogen vertices.

The dimension of time has been added to the disease triangle by several authors (1,6) to convey the impression that disease onset and intensity are affected by the duration that the three factors are aligned. Naturally, disease may not happen in the first instant the three parameters are aligned favorably but will occur after some duration. The demarcation between a healthy and a diseased plant is one not easily drawn. Indeed, symptoms and signs can take a good deal of time to appear but physiological events that define infection usually take minutes to hours. To show time as a vertex on a pyramid may be instructive; however, unlike the other three triangular elements, time is an invariant and unidirectional vector. Thus, illustration of time as a dimension rather than as a point on an arbitrary axis is more realistic and in fact may confer more educational value. Browning et al. (2) illustrated much the same idea with a disease cone (Figure 4), a figure which expanded through time and whose volume and final area at the end of the epidemic was dependent on the states of the three interacting variables. Once again, disease was represented as a quantity in Browning's treatment.

Figure 4. The disease cone after Browning (1). This variant of the disease triangle showed expansion of disease intensity through time.

Figure 5. A right angle prism, which is an alternative to the disease pyramid and cone for the representation of the dimension of time.

Time is represented as the z axis in Figure 5, which shows the continuous existence of a disease triangle as a right angle prism. The prism may be considered as representing disease in a quantitative manner (i.e., intensity) or qualitatively as a persistent phenomenon. Time can be collapsed to near zero by slicing the prism perpendicular to the z axis; this reduces the figure to the original disease triangle (i.e., differentiation with respect to the temporal plane). The disease triangle is thus a snapshot of the relationship at some instant in time (Figure 6).

Figure 6. A series of triangles sequentially stacked to show development of plant disease through time. Figure 5 may be considered as an integral of this series.

|Advanced pedagogical training and biological realism can be derived by allowing flexible connections to substitute for straight lines. This approach allows for change in each element over time and quantitative disease expression. Further, the process of disease onset can be shown as arising from a point and expanding to reach the familiar triangle, much as the disease cone does (2). Moreover, the area under the disease progress curve, a basic epidemiological parameter (3), would be essentially analogous to measuring the integral of stacked triangles (Figure 6).

One can also extend the idea of flexible connectivity to allow for both inward and outward bending of the triangle's sides. For example, environment can become unfavorable during certain times, leading to interrupted disease development and a markedly constricted triangle. In the same sense, the maximum outward bowing of a line can illustrate the biological potential of the system. A region of expansion may be understood in several ways: for example, as the spread of dysfunction through several levels of biological organization (binding of biochemicals, alteration of physiological pathways, cellular disruption, programmed cell death, visible symptoms); as the appearance of disease only when the triangle passes a defined threshold in time (disease onset); or, from a quantitative population perspective, the increase in disease incidence among individuals.

The disease triangle will almost certainly be an educational paradigm in the discipline of plant pathology for many years to come. One hopes the discussion here will enhance the educational value of the triangle and its variants.